Question

Convergence of this series?

Answer 1

\[\sum_{n=1}^{\infty} 1/ (n+ ncos^2 (n))\]

Answer 2

Which could simplify into \[\sum_{n=1}^{\infty} 1/ (n+1) \cos^2(n)\]

Answer 3

And -1=<cos^2(n) =< 1

Answer 4

I don't see how you did that simplification

Answer 5

Shouldn't it be
\[\frac{ 1 }{ n(1 + \cos^2 n) }\]

Answer 6

Yes sorry, that was a mistake.

Answer 7

I think this diverges because of the 1/n

Answer 8

Yeah, I got it now. Thanks (: But can you separate a constant from a series no matter its convergence or divergence?

Answer 9

if it is like a series of 1/3n can we say that equates to 1/3 * series of 1/n

Answer 10

Yes

Answer 11

Ok thanks

Answer 12

yw